N. Kroemer, S.G. Wicha
Dept. of Clinical Pharmacy, Institute of Pharmacy, University of Hamburg, Hamburg, Germany
Objectives: In pharmacodynamic (PD) interaction screening elucidation of the nature of the PD interaction (synergy, antagonism, additivity) is essential. Checkerboard assays are a common method for in vitro testing, but usually require a high number of drug concentrations to be studied. The objective of the present study was to in silico develop a reduced optimal design approach to identify the PD interaction accurately and efficiently to allow high-throughput in vitro testing of antibiotic combinations.
Base for the estimation of parameters was a simplified general pharmacodynamic interaction (GPDI) model [1], which not only identifies the type of the interaction (synergistic (syn), antagonistic (ant), asymmetric (2d)), but also considers the direction of the interaction by identifying perpetrator and victim drugs.
Conventional schemes usually cover 9×9 tested concentrations based on two-fold increments of minimum inhibitory concentrations (MIC). An optimized design using 3×3 concentrations based on effective concentration (EC) values was proposed earlier providing similar information as the conventional design but being considerably more efficient [2]. In this study we investigated, if the number of concentrations could be further reduced to 2×2 designs using a D-optimal design approach. First, a quadratic 2×2 design was evaluated, in a second step a rhombic 2×2 design was developed and compared to the earlier proposed 3×3 design.
Methods: Experimental design evaluations and optimization studies were performed using the GPDI model implemented in ‘R’ [3]. To simplify the calculations, the interaction potency was fixed to EC50.
For development of reduced checkerboard designs 1000 parameter sets of two fictive drugs A and B for each type of interaction were sampled. A combination of the two algorithms Nelder-Mead [4] and L-BFGS-B [5] was used to evaluate optimal combinations of EC-parameters for each parameter set. The inverse value of the determinate of the Fisher information matrix was used as objective function to be minimized by the EC concentrations as design variables.
For both designs one optimized EC combination was selected and reevaluated via calculation of the expected relative standard errors (RSE) estimated from the GPDI model [1] by again sampling 1000 random combinations of two simulated drugs A and B.
Median and 95% confidence intervals (CI) of the RSE’s were calculated to compare the three design approaches.
Results: The EC parameter sets for both design approaches were picked as a compromise leading to low expected RSE in all three interaction scenarios to identify all interaction types with maximum reliability. For the reference 3×3 design the parameters were EC20, EC50, EC80, for the 2×2 quadratic design EC20 and EC85 were picked and for the 2×2 rhombic design EC10/EC45, EC45/EC10, EC45/EC85, EC85/EC45 were the chosen EC combinations.
The median RSEs and CI were similar between the interaction parameters directional from drug A to B and B to A, hence just the results for the interaction parameters for drug A affected by drug B are shown.
Comparing the three designs, the richer 3×3 design allowed the lowest median RSEs and therefore it is the experimental design, which is able to calculate the interaction parameters most accurately (Median [2.5% and 97.5% CI], AB-syn: 69.20 [12.01; 476.88], AB-ant: 11.43 [5.62; 35.74], AB-2d: 28.59 [7.17; 225.83]). The sparser quadratic 2×2 and rhombic design resulted in higher expected RSE, but a in lower spread of RSE for the rhombic design. Quadratic: AB-syn: 87.10 [12.52; 720.60], AB-ant: 16.17 [7.50; 65.44], AB-2d: 47.62 [8.89; 371.73]. Rhombic: AB-syn: 82.88 [22.51; 386.27], AB-ant: 16.15 [7.88; 53.08], AB-2d: 40.75 [9.87; 230.29].
Conclusions: With more than halving the number of concentrations to be studied, no scheme could be developed, which leads to comparable RSE as the 3×3 design. However, the developed rhombic 2×2 design enables gaining information more precisely than both quadratic designs (2×2, 3×3), when comparing the ranges of the RSE-CIs based on the median. Although the reduced designs were not as reliable as the 3×3 design, they can provide information about the interaction type and could be used as a pretest in high throughput screening to elucidate the nature of the PD interaction. Application of the rhombic 2×2 design is warranted to elucidate the practicability of the design in PD interaction testing.
References:
[1] S. G. Wicha, C. Chen, O. Clewe, and U. S. H. Simonsson, “A general pharmacodynamic interaction model identifies perpetrators and victims in drug interactions.,” Nat. Commun., vol. 8, no. 1, p. 2129, Dec. 2017, doi: 10.1038/s41467-017-01929-y.
[2] C. Chen, S. G. Wicha, R. Nordgren, and U. S. H. Simonsson, “Comparisons of Analysis Methods for Assessment of Pharmacodynamic Interactions Including Design Recommendations,” AAPS J., vol. 20, no. 4, p. 77, Jul. 2018, doi: 10.1208/s12248-018-0239-0.
[3] R Core Team (2019), “R: A language and environment for statistical computing.” R Foundation for Statistical Computing, Vienna, Austria.
[4] J. A. Nelder and R. Mead, “A Simplex Method for Function Minimization,” Comput. J., vol. 7, no. 4, pp. 308–313, Jan. 1965, doi: 10.1093/comjnl/7.4.308.
[5] R. H. Byrd, P. Lu, J. Nocedal, and C. Zhu, “A Limited Memory Algorithm for Bound Constrained Optimization,” SIAM J. Sci. Comput., vol. 16, no. 5, pp. 1190–1208, Sep. 1995, doi: 10.1137/0916069.
Reference: PAGE () Abstr 9387 [www.page-meeting.org/?abstract=9387]
Poster: Study Design